Spin-constrained Hartree-Fock and the generator coordinate method for the 2-site Hubbard model

We present a mathematical analysis of the spin-constrained Hartree-Fock solutions (CHF) of the 2-site Hubbard model. The analysis sheds light on the spin symmetry breaking process around the Coulson-Fischer point. CHF states are useful as input states for the Generator Coordinate Method (GCM) in which CHF states can be used as a basis for multiconfigurational calculations in the Hill-Wheeler equations. The spin degree of freedom provides the generator coordinate in the GCM related to static electron correlation.